Considering mechanics
from a variational point of view goes back to Euler, Lagrange
and Hamilton. The form of the variational principle most important
for continuous mechanics is due to Hamilton, and is often called
Hamiltonís principle or the least action principle. Modern geometric mechanics
stimulated from the work of Arnold, Marsden and their coworkers. This application
of geometrically based ideas to a concrete physical problem is very much in the spirit
of Poincare's work in classical mechanics.
Despite its maturity, geometric mechanics
continuous to grow and find application in various areas. In particular, it finds application
in the study of complex materials, nonholonomic mechanics, discrete and stochastic mechanics.
They playskip a significant role in the theory of integrable systems and symmetry analysis of physics.